A309101 Primes whose decimal representation can be written as a sequence of primes separated by single zeros.

307, 503, 1103, 1303, 1307, 1907, 2011, 2017, 2029, 2053, 2083, 2089, 2903, 3011, 3019, 3023, 3037, 3041, 3061, 3067, 3079, 3083, 3089, 4703, 5011, 5023, 5059, 5303, 5903, 6703, 7013, 7019, 7043, 7079, 7103, 7307, 7907, 10103, 10303, 10903, 11047, 11059, 11071, 11083

Offset: 1

Author

Bernard Schott, Jul 12 2019

Keywords

• nonn
• base
• nice

Comments

In the Honaker-Caldwell link there is the example

2030507011013017019023029031037041043047053059061067071073079083089097

with 70 digits. It consists of the sequence of primes less than 100 separated by zeros.

Examples

			10103 is a term because 101 and 3 are primes separated by a single zero.
		

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 20305...89097 (70-digits)

Crossrefs

Cf. A000040.

Programs

Mathematica

Take[Select[FromDigits[Flatten[IntegerDigits/@#]]&/@(Riffle[#,0]&/@Tuples[Prime[ Range[ 30]],2]),PrimeQ]//Sort,50] (* Harvey P. Dale, Jul 05 2022 *)

PARI

cut(d, b) = {my(nb = hammingweight(b), vs = vector(nb+1, k, ""), iz = 0, ind = 1); for (i=1, #d, if (d[i] == 0, iz ++; if (b[iz], ind++, vs[ind] = concat(vs[ind], d[i])), vs[ind] = concat(vs[ind], d[i]););); apply(x->eval(x), vs);}
isok(n) = {if (isprime(n), my(d = digits(n), dz = select(x->(x==0), d, 1), nbz = #dz); if (! nbz, return (0)); if (nbz > 1, for (k=2, #dz, if (dz[k] == dz[k-1] + 1, return (0)););); for (i=1, 2^nbz-1, my(b = binary(i)); while (#b < nbz, b = concat(0, b)); my(vstr = cut(d, b)); if (#select(x->isprime(x), vstr) == #vstr, return (1));););} \\ Michel Marcus, Aug 07 2019

Extensions

Missing term 10903 and more terms from Michel Marcus, Aug 07 2019